Synchronization of an optical frequency comb and a microwave oscillator with 53 zs/Hz^1/2 resolution and 10^-20-level stability

Abstract

Precise and stable synchronization between an optical frequency comb (femtosecond mode-locked laser oscillator or microresonator-based comb) and a microwave oscillator is important for various fields including telecommunication, radio astronomy, metrology, and ultrafast X-ray and electron science. Timing detection and synchronization using electro-optic sampling with an interferometer has been actively used for low-noise microwave generation, long-distance timing transfer, comb stabilization, time-of-flight sensing, and laser-microwave synchronization for ultrafast science facilities. Despite its outstanding performance, there has been a discrepancy in synchronization performance of more than 10 dB between the projected shot-noise-limited noise floor and the measured residual noise floor. In this work, we demonstrate the shot-noise-limited performance of an electro-optic timing detector-based comb-microwave synchronization, which enabled an unprecedented residual phase noise floor of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m1"> <mml:mrow> <mml:mo form="prefix">−</mml:mo> <mml:mn>174.5</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>dBc</mml:mi> <mml:mo>/</mml:mo> <mml:mi>Hz</mml:mi> </mml:mrow> </mml:math> at 8 GHz carrier frequency (i.e., <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m2"> <mml:mrow> <mml:mn>53</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>zs</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>Hz</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> timing noise floor), integrated rms timing jitter of 88 as ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m3"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>Hz</mml:mi> <mml:mtext> </mml:mtext> <mml:mi>to</mml:mi> <mml:mtext> </mml:mtext> <mml:mn>1</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>MHz</mml:mi> </mml:mrow> </mml:math> ), rms timing drift of 319 as over 12 h, and frequency instability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="m4"> <mml:mrow> <mml:mn>3.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> over 10,000 s averaging time. We identified that bandpass filtering of the microwave signal and optical pulse repetition-rate multiplication are critical for achieving this performance.